B. Neyshabur, S. Bhojanapalli, and N. Srebro. A PAC-bayesian approach to spectrally-normalized margin bounds for neural networks. In International Conference on Learning Representations, 2018.
C. Pabbaraju, E. Winston, and J. Z. Kolter. Estimating lipschitz constants of monotone deep equilibrium models. In International Conference on Learning Representations, 2021.
B. G. Pachpatte and W. Ames. Inequalities for Differential and Integral Equations. Elsevier, 1997.
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala. PyTorch: An Imperative Style, High-Performance Deep Learning Library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
Z. Qian, W. Zame, L. Fleuren, P. Elbers, and M. van der Schaar. Integrating expert ODEs into neural ODEs: Pharmacology and disease progression. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P. S. Liang, and J. W. Vaughan, editors, Advances in Neural Information Processing Systems, volume 34. Curran Associates, Inc., 2021.
A. F. Queiruga, N. B. Erichson, D. Taylor, and M. W. Mahoney. Continuous-in-depth neural networks. arXiv preprint arXiv:2008.02389, 2020.
A. F. Queiruga, N. B. Erichson, L. Hodgkinson, and M. W. Mahoney. Stateful ODE-nets using basis function expansions. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. W. Vaughan, editors, Advances in Neural Information Processing Systems, volume 34. Curran Associates, Inc., 2021.
M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686-707, 2019.
M. E. Sander, P. Ablin, and G. Peyre. Do residual neural networks discretize neural ordinary differential equations? In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 35. Curran Associates, Inc., 2022.
M. Thorpe and Y. van Gennip. Deep limits of residual neural networks. Research in the Mathematical Sciences, 10(1):6, 2022.
B. Tzen and M. Raginsky. Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit. arXiv preprint arXiv:1905.09883, 2019.
M. J. Wainwright. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge University Press, 2019.
Y. Yin, I. Ayed, E. de Bézenac, N. Baskiotis, and P. Gallinari. LEADS: Learning dynamical systems that generalize across environments. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P. S. Liang, and J. W. Vaughan, editors, Advances in Neural Information Processing Systems, volume 34. Curran Associates, Inc., 2021.
D. Yu, H. Miao, and H. Wu. Neural generalized ordinary differential equations with layer-varying parameters. arXiv preprint arXiv:2209.10633, 2022.
F. Zhou, L. Li, K. Zhang, and G. Trajcevski. Urban flow prediction with spatial-temporal neural ODEs. Transportation Research Part C: Emerging Technologies, 124:102912, 2021.